Search results for "General Computer Science"
showing 10 items of 895 documents
Circular sturmian words and Hopcroft’s algorithm
2009
AbstractIn order to analyze some extremal cases of Hopcroft’s algorithm, we investigate the relationships between the combinatorial properties of a circular sturmian word (x) and the run of the algorithm on the cyclic automaton Ax associated to (x). The combinatorial properties of words taken into account make use of sturmian morphisms and give rise to the notion of reduction tree of a circular sturmian word. We prove that the shape of this tree uniquely characterizes the word itself. The properties of the run of Hopcroft’s algorithm are expressed in terms of the derivation tree of the automaton, which is a tree that represents the refinement process that, in the execution of Hopcroft’s alg…
Nondeterministic Moore automata and Brzozowski's minimization algorithm
2012
AbstractMoore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. We propose an algorithm that is a variant of Brzozowski’s minimization algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice. Moreover, we explore more general classes of NMA and analyze the applicability of the algorithm. For some of such classes the algorith…
Standard Sturmian words and automata minimization algorithms
2015
The study of some close connections between the combinatorial properties of words and the performance of the automata minimization process constitutes the main focus of this paper. These relationships have been, in fact, the basis of the study of the tightness and the extremal cases of Hopcroft's algorithm, that is, up to now, the most efficient minimization method for deterministic finite state automata. Recently, increasing attention has been paid to another minimization method that, unlike the approach proposed by Hopcroft, is not based on refinement of the set of states of the automaton, but on automata operations such as determinization and reverse, and is also applicable to non-determ…
Extremal minimality conditions on automata
2012
AbstractIn this paper we investigate the minimality problem of DFAs by varying the set of final states. In other words, we are interested on how the choice of the final states can affect the minimality of the automata. The state-pair graph is a useful tool to investigate such a problem. The choice of a set of final states for the automaton A defines a coloring of the closed components of the state-pair graph and the minimality of A corresponds to a property of these colored components. A particular attention is devoted to the analysis of some extremal cases such as, for example, the automata that are minimal for any choice of the subset of final states F from the state set Q of the automato…
A graph theoretic approach to automata minimality
2012
AbstractThe paper presents a graph-theoretic approach to test the minimality of a deterministic automaton. In particular, we focus on problems concerning the dependence of the minimality of an automaton on the choice of the set F of final states or on the cardinality of the set F. We introduce different minimality conditions of an automaton and show that such conditions can be characterized in graph-theoretic terms.
Theory of tailor automata
2019
Abstract In the paper, a fragment of the new theory of tailor automata is presented, within which a deterministic finite automaton was defined. The proposed automaton provides a theoretical model of an informally characterized biomolecular automaton. The idea of working of which is founded on the concept of alternating cut of some double-stranded fragments of DNA, with the use of a restriction enzyme and ligations of some double-stranded fragments of DNA, with the use of the ligase enzyme.
Timed Sets, Functional Complexity, and Computability
2012
AbstractThe construction of various categories of “timed sets” is described in which the timing of maps is considered modulo a “complexity order”. The properties of these categories are developed: under appropriate conditions they form discrete, distributive restriction categories with an iteration. They provide a categorical basis for modeling functional complexity classes and allow the development of computability within these settings. Indeed, by considering “program objects” and the functions they compute, one can obtain models of computability – i.e. Turing categories – in which the total maps belong to specific complexity classes. Two examples of this are introduced in some detail whi…
A genetic system based on simulated crossover of sequences of two-bit genes
2006
AbstractWe introduce a genetic model based on simulated crossover of fixed sequences of two-bit genes. Results are(1)a lower bound on population size is exhibited such that a transition takes the stochastic finite population genetic system near the next state of the deterministic infinite population genetic system (provided both begin in the same state);(2)states and dynamics of the deterministic infinite population genetic system are derived for arbitrary (finite) fitness functions (expressed in terms of multivariate polynomials);(3)in the case of quadratic fitness defined by weight matrices with m nonnull entries it is shown that each state transition can be implemented in time O(m+l), wh…
XML document-grammar comparison: related problems and applications
2011
10.2478/s13537-011-0005-1; International audience; XML document comparison is becoming an ever more popular research issue due to the increasingly abundant use of XML. Likewise, a growing interest fosters the development of XML grammar matching and comparison, due to the proliferation of heterogeneous XML data sources, particularly on the Web. Nonetheless, the process of comparing XML documents with XML grammars, i.e., XML document and grammar similarity evaluation, has not yet received the attention it deserves. In this paper, we provide an overview on existing research related to XML document/grammar comparison, presenting the background and discussing the various techniques related to th…
An overview on XML similarity: Background, current trends and future directions
2009
In recent years, XML has been established as a major means for information management, and has been broadly utilized for complex data representation (e.g. multimedia objects). Owing to an unparalleled increasing use of the XML standard, developing efficient techniques for comparing XML-based documents becomes essential in the database and information retrieval communities. In this paper, we provide an overview of XML similarity/comparison by presenting existing research related to XML similarity. We also detail the possible applications of XML comparison processes in various fields, ranging over data warehousing, data integration, classification/clustering and XML querying, and discuss some…